In a field such as an automatic control, there is an issue of identification of a linear system. For example, when an analogue input u(t) and an analogue output y(t) are given with respect to a physical system, which is represented by a linear ordinary differential equation as illustrated in FIG. 1, a problem is to determine differential coefficients P1 to Pm of differential operators P(d/dt) so that the following relations hold.
                    P        ⁡                  (                      d                          d              ⁢                                                          ⁢              t                                )                    ⁢              y        ⁡                  (          t          )                      =          u      ⁡              (        t        )                        P      ⁡              (                  d                      d            ⁢                                                  ⁢            t                          )              =                            (                      d                          d              ⁢                                                          ⁢              t                                )                m            +                                    P            1                    ⁡                      (                          d                              d                ⁢                                                                  ⁢                t                                      )                                    m          -          1                    +      …      +                        P                      m            -            1                          ⁡                  (                      d                          d              ⁢                                                          ⁢              t                                )                    +              P        m            
In this patent application, a case where P(d/dt) y(t) is almost equal to u(t) is represented as P(d/dt)y(t) being equal to u(t).
However, sensor values such as output values of an accelerometer, which is recently used, are digital values (i.e. discrete values) instead of analogue values. Therefore, as illustrated in FIG. 2, when digital inputs u0, u1, u2n and digital outputs y0, y1, . . . , y2n are given, a method for determining differential coefficients P1 to Pm of the differential operators P(d/dt) is considered so that the differential equation P(d/dt)y(t)=u(t) of the physical system, which is represented by the ordinary differential equation, holds.
Therefore, in order to realize this, the digital data is converted to the analogue data. As for that method, there is a fitting method. The spline method is a conventional famous fitting method, however, it has a problem that it is possible to differentiate the spline curve a few times, for example. Therefore, when order m of the differential operator is high, the spline method cannot be applied.
Moreover, even when another fitting method is adopted, it is not realistic in view of the calculation amount that the differential operations are calculated for all times, and it is not possible to identify the system that is represented by the differential equation including higher-order differential operators.    Patent Document 1: Japanese Laid-open Patent Publication No. 2013-175143    Patent Document 2: Japanese Laid-open Patent Publication No. 2010-264499    Patent Document 3: Japanese Laid-open Patent Publication No. 2000-182552    Patent Document 4: Japanese Laid-open Patent Publication No. 2003-108542    Patent Document 5: Japanese Laid-open Patent Publication No. 2007-286801    Patent Document 6: Japanese Laid-open Patent Publication No. 2001-208842    Non-Patent Document 1: T. Ito, Y. Senta and F. Nagashima, “Analyzing Bilinear Neural Networks with New Curve Fitting for Application to Human Motion Analysis”, in Proc. IEEE Int. Conf. Systems, Man and Cybernetics, 2012, pp. 345-352